Plot points P (1,0), Q (4,0) and S (1,3) . coordinates of point R such that PQRS is a square.

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3. Coordinate Geometry

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Plot the points $P (1,0), Q (4,0)$ and $S (1,3) .$ Find the coordinates of the point $R$ such that $PQRS$ is a square.

Option A

Option B

Option C

Option D

Solution

Plot the points $P (1,0), Q(4,0)$ and $S (1,3)$ in the Cartesian plane. As we know all the sides of a square are equal and each angle is of $90^{\circ}$ measure. Therefore, the abscissa of the vertex $R$ is $4$ and its ordinate is $3 .$

Hence, the coordinate of the point $R$ are $(4,3)$

Standard 9

Mathematics

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$(ii)$ whose ordinate is $-4$ and which lies on $y$ -axis.

$(iii)$ whose abscissa is $5$ and which lies on $x$ -axis.

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Plot the points $P (1,0), Q (4,0)$ and $S (1,3) .$ Find the coordinates of the point $R$ such that $PQRS$ is a square.

Solution

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Find the coordinates of the point

$(i)$ which lies on $x$ and $y$ axes both.

$(ii)$ whose ordinate is $-4$ and which lies on $y$ -axis.

$(iii)$ whose abscissa is $5$ and which lies on $x$ -axis.